Finite Group Databasebeta

← #25007375

Subgroups — #25007375

Order 11008.

464 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 464 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19140484C211yesmaximal, characteristic
2#19134582C211yesmaximal, characteristic, complemented
3#19132934C211yesmaximal, characteristic, complemented
4#19132620C211yesmaximal, characteristic, complemented
5#19132618C211yesmaximal, characteristic, complemented
6#19132592C211yesmaximal, characteristic, complemented
7C43×#1343C211yesmaximal, characteristic, complemented
8C2×#13063296C411yescharacteristic, complemented
9C2×(C22⋊D43)⋊C4C2211yescharacteristic
10#14582953—21no—
11C2×#13063239—21no—
12#14582839C411yescharacteristic, complemented
13#14582835C2211yescharacteristic
14#14582814—21no—
15#14582813C411yescharacteristic, complemented
16#14582807—21no—
17#14582793—21no—
18#14582779—21no—
19#14582761C411yescharacteristic, complemented
20#14582757—21no—
21#14582666C2211yescharacteristic
22#14582623C2211yescharacteristic
23#14582622—21no—
24C43×#392C2211yescharacteristic
25C43×#342C2211yescharacteristic
26C43×#323C2211yescharacteristic
27C22×C22⋊D43—21no—
28C22×C22⋊D43D411yescharacteristic
29C23×Dic43D411yescharacteristic
30C22×C4×D43C2×C411yescharacteristic
31#13063296—41no—
32#13063296—41no—
33(C22⋊D43)⋊C4—41no—
34(C22⋊D43)⋊C4—41no—
35C2×C4⋊Dic43C2×C411yescharacteristic
36C2×Dic43⋊C4—21no—
37C2×Dic43⋊C4—41no—
38C2×Dic43⋊C4C2×C411yescharacteristic
39C2×C22⋊Dic43—21no—
40C2×C22⋊Dic43—21no—
41C2×C22⋊Dic43—21no—
42C2×C22⋊Dic43—21no—
43C2×C22⋊Dic43—21no—
44C2×(C2×D43)⋊C4—21no—
45C2×(C2×D43)⋊C4D411yescharacteristic
46C2×C4×Dic43D411yescharacteristic
47Dic43⋊C8—41no—
48#13063239—42no—
49C22⋊(C43⋊C8)—21no—
50#13063235—41no—
51C43⋊#95—21no—
52C43⋊#95—21no—
53C43⋊#95—21no—
54C43⋊#95—41no—
55C43⋊#95C2×C411yescharacteristic
56C22×D4×C43—21no—
57C22×D4×C43C2×C411yescharacteristic
58C2×C22⋊C4×C43—21no—
59C2×C22⋊C4×C43—21no—
60C2×C22⋊C4×C43C2311yescharacteristic
61C22⋊C8×C43—21no—
62#95×C43C2×C411yescharacteristic
63C24×C43—21no—
64C24×C43C2×D411yescharacteristic
65C23×D43C22⋊C411yescharacteristic
66C2×D4×C43—41no—
67C2×D4×C43—41no—
68C2×D4×C43—41no—
69C2×D4×C43—81no—
70C2×D4×C43—81no—
71C2×D4×C43—81no—
72C22×C4×C43—21no—
73C22×C4×C43—41no—
74C22×C4×C43C22×C411yescharacteristic
75C22×C4×C43C2×D411yescharacteristic
76C2×C22⋊D43—21no—
77C2×C22⋊D43—21no—
78C2×C22⋊D43—41no—
79C2×C22⋊D43—41no—
80C2×C22⋊D43—42no—
81C2×C22⋊D43—81no—
82C2×C22⋊D43—81no—
83C22×Dic43—21no—
84C22×Dic43—21no—
85C22×Dic43—21no—
86C22×Dic43—21no—
87C22×Dic43—41no—
88C22×Dic43—81no—
89C22×Dic43C22⋊C411yescharacteristic
90C22×Dic43C22⋊C411yescharacteristic
91C22×Dic43C22⋊C411yescharacteristic
92C2×C4×D43—21no—
93C2×C4×D43—21no—
94C2×C4×D43—81no—
95C2×C8×C43—41no—
96C22⋊C4×C43—41no—
97C22⋊C4×C43—41no—
98C22⋊C4×C43—41no—
99C22⋊C4×C43—81no—
100C22⋊Dic43—41no—
101C22⋊Dic43—42no—
102C22⋊Dic43—41no—
103C22⋊Dic43—41no—
104C22⋊Dic43—41no—
105C22⋊Dic43—81no—
106C22⋊Dic43—81no—
107(C2×D43)⋊C4—41no—
108(C2×D43)⋊C4—81no—
109C4⋊Dic43—41no—
110Dic43⋊C4—41no—
111Dic43⋊C4—81no—
112Dic43⋊C4—82no—
113C4×Dic43—21no—
114C4×Dic43—21no—
115C2×C43⋊C8—41no—
116C23×C43—21no—
117C23×C43—21no—
118C23×C43—41no—
119C23×C43—41no—
120C23×C43—41no—
121C23×C43—41no—
122C23×C43—41no—
123C23×C43—41no—
124C23×C43—41no—
125C23×C43—41no—
126C23×C43—41no—
127C23×C43C2×C22⋊C411yescharacteristic
128C23×C43AGL(1,ℤ/8)11yescharacteristic
129C23×C43#13711yescharacteristic
130C22×D43—21no—
131C22×D43—21no—
132C22×D43—21no—
133C22×D43—41no—
134C22×D43—41no—
135D4×C43—82no—
136D4×C43—82no—
137D4×C43—82no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—41no—
141C2×C4×C43—41no—
142C2×C4×C43—41no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—81no—
146C2×C4×C43—81no—
147C2×C4×C43—81no—
148C22⋊D43—42no—
149C22⋊D43—42no—
150C22⋊D43—84no—
151C2×Dic43—21no—
152C2×Dic43—21no—
153C2×Dic43—21no—
154C2×Dic43—21no—
155C2×Dic43—41no—
156C2×Dic43—42no—
157C2×Dic43—41no—
158C2×Dic43—41no—
159C2×Dic43—41no—
160C2×Dic43—41no—
161C2×Dic43—41no—
162C2×Dic43—41no—
163C2×Dic43—41no—
164C2×Dic43—81no—
165C2×Dic43—81no—
166C2×Dic43—81no—
167C2×Dic43—81no—
168C2×Dic43#9911yescharacteristic
169C2×Dic43#9911yescharacteristic
170C4×D43—81no—
171C4×D43—81no—
172C8×C43—81no—
173C43⋊C8—81no—
174#11824—431nomaximal, Sylow
175C22×C43—21no—
176C22×C43—21no—
177C22×C43—21no—
178C22×C43—21no—
179C22×C43—41no—
180C22×C43—41no—
181C22×C43—41no—
182C22×C43—41no—
183C22×C43—81no—
184C22×C43—81no—
185C22×C43—81no—
186C22×C43—81no—
187C22×C43—81no—
188C22×C43—81no—
189C22×C43—81no—
190C22×C43—81no—
191C22×C43C2×#9911yescharacteristic
192C22×C43#41711yescharacteristic
193C22×C43#42111yescharacteristic
194C2×D43—41no—
195C2×D43—41no—
196C2×D43—41no—
197C2×D43—81no—
198C2×D43—81no—
199C4×C43—41no—
200C4×C43—41no—
201C4×C43—81no—
202C4×C43—161no—
203Dic43—21no—
204Dic43—21no—
205Dic43—41no—
206Dic43—41no—
207Dic43—81no—
208Dic43—81no—
209Dic43—161no—
210#2635—431no—
211#1799—431no—
212#1466—431no—
213#1352—431no—
214#1352—431no—
215#1343—431no—
216#1343D4311yescharacteristic, complemented
217C2×C43—21no—
218C2×C43—21no—
219C2×C43—41no—
220C2×C43—41no—
221C2×C43—161no—
222C2×C43#151311yescharacteristic
223C2×C43#212111yescharacteristic
224C2×C43#212811yescharacteristic
225D43—81no—
226C2×#121—431no—
227C2×C4×D4—431no—
228#432—861no—
229C2×#99—861no—
230#400—431no—
231#399—431no—
232#394—431no—
233#394—861no—
234#392—861no—
235#392C2×D4311yescharacteristic
236#388—861no—
237#386—861no—
238#381—431no—
239#380—861no—
240#342—431no—
241#342C2×D4311yescharacteristic
242#323—431no—
243#323—861no—
244#323C2×D4311yescharacteristic
245C43#1182411yescharacteristic, complemented, Sylow
246C22×D4—21no—
247C22×D4—431no—
248C22×D4—861no—
249C22×D4C4×D4311yescharacteristic
250C23×C4—431no—
251C23×C4—431no—
252#121—1721no—
253#121—1721no—
254C4×D4—1721no—
255C4×D4—1721no—
256C2×C4⋊C4—431no—
257C2×C4⋊C4—431no—
258C2×C4⋊C4—861no—
259C2×C4⋊C4—1721no—
260C2×C22⋊C4—21no—
261C2×C22⋊C4—21no—
262C2×C22⋊C4—431no—
263C2×C22⋊C4—861no—
264C2×C22⋊C4—861no—
265C2×C22⋊C4—861no—
266C2×C22⋊C4—861no—
267C2×C22⋊C4—861no—
268C2×C22⋊C4—861no—
269C2×C22⋊C4C22×D4311yescharacteristic
270C2×C42—431no—
271C4⋊C8—1721no—
272#99—1722no—
273C22⋊C8—21no—
274C22⋊C8—861no—
275#97—1721no—
276#95—431no—
277#95—861no—
278#95—861no—
279#95—861no—
280#95—1721no—
281#95C4×D4311yescharacteristic
282C24—21no—
283C24—431no—
284C24D4×D4311yescharacteristic
285C2×D4—41no—
286C2×D4—41no—
287C2×D4—41no—
288C2×D4—81no—
289C2×D4—81no—
290C2×D4—81no—
291C2×D4—861no—
292C2×D4—861no—
293C2×D4—3441no—
294C2×D4—3441no—
295C2×D4—1721no—
296C2×D4—1721no—
297C2×D4—1722no—
298C22×C4—21no—
299C22×C4—41no—
300C22×C4—431no—
301C22×C4—431no—
302C22×C4—431no—
303C22×C4—861no—
304C22×C4—861no—
305C22×C4—861no—
306C22×C4—861no—
307C22×C4—861no—
308C22×C4—861no—
309C22×C4—3441no—
310C22×C4—3441no—
311C22×C4—1721no—
312C22×C4C2×C4×D4311yescharacteristic
313C22×C4D4×D4311yescharacteristic
314C2×C8—41no—
315C2×C8—1721no—
316C4⋊C4—3441no—
317C4⋊C4—3442no—
318C4⋊C4—1721no—
319C4⋊C4—1721no—
320C22⋊C4—41no—
321C22⋊C4—41no—
322C22⋊C4—41no—
323C22⋊C4—81no—
324C22⋊C4—3441no—
325C22⋊C4—3441no—
326C22⋊C4—3441no—
327C22⋊C4—1721no—
328C22⋊C4—1721no—
329C22⋊C4—1721no—
330C22⋊C4—1722no—
331C22⋊C4—1721no—
332C22⋊C4—1721no—
333C42—861no—
334C42—861no—
335C23—21no—
336C23—21no—
337C23—41no—
338C23—41no—
339C23—41no—
340C23—41no—
341C23—41no—
342C23—41no—
343C23—41no—
344C23—41no—
345C23—41no—
346C23—861no—
347C23—861no—
348C23—861no—
349C23—1721no—
350C23—1721no—
351C23C22⋊C4×D4311yescharacteristic
352C23#1306334911yescharacteristic
353C23#1306335411yescharacteristic
354D4—82no—
355D4—82no—
356D4—82no—
357D4—3444no—
358D4—1722no—
359D4—1722no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—41no—
363C2×C4—41no—
364C2×C4—41no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—81no—
368C2×C4—81no—
369C2×C4—81no—
370C2×C4—431no—
371C2×C4—431no—
372C2×C4—861no—
373C2×C4—861no—
374C2×C4—861no—
375C2×C4—861no—
376C2×C4—3441no—
377C2×C4—3441no—
378C2×C4—3441no—
379C2×C4—3441no—
380C2×C4—3441no—
381C2×C4—3441no—
382C2×C4—1721no—
383C2×C4—1722no—
384C2×C4—1721no—
385C2×C4—1721no—
386C2×C4—1721no—
387C2×C4—1721no—
388C2×C4—1721no—
389C2×C4—1721no—
390C2×C4—1721no—
391C8—81no—
392C8—3441no—
393C22—21no—
394C22—21no—
395C22—21no—
396C22—21no—
397C22—41no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—81no—
402C22—81no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—81no—
407C22—81no—
408C22—81no—
409C22—3441no—
410C22—3441no—
411C22—1721no—
412C22—1721no—
413C22—1721no—
414C22#99×D4311yescharacteristic
415C22#1458289711yescharacteristic
416C22#1458291411yescharacteristic
417C4—41no—
418C4—41no—
419C4—81no—
420C4—161no—
421C4—861no—
422C4—861no—
423C4—3441no—
424C4—3441no—
425C4—1721no—
426C4—1721no—
427C4—6881no—
428C2—21no—
429C2—21no—
430C2—41no—
431C2—41no—
432C2—161no—
433C2—3441no—
434C2#1913313511yescharacteristic
435C2#1913623811yescharacteristic
436C2#1913626511yescharacteristic
subgroupG/H
centerC22#99×D43
commutatorC22×C4×C43C22×C4
FrattiniC2×C22⋊C4C22×D43
FittingC43×#1343C2
socleC22×C43C2×#99
prime radical#19140484C2
cosocleC2×C22⋊C4×C43C23
hypercenter#1343D43
hypocenterC43#11824
LCSG ▷ C22×C4×C43 ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #1343

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #19134582C2semidirect
3. #19132934C2semidirect
4. #19132620C2semidirect
5. #19132618C2semidirect
6. #19132592C2semidirect
7. C43×#1343C2semidirect
8. C2×#13063296C4semidirect
12. #14582839C4semidirect
15. #14582813C4semidirect
19. #14582761C4semidirect
216. #1343D43semidirect
245. C43#11824semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191404842
#191345822
#191329342
#191326202
#191326182
#191325922
C43×#13432
#1182443